Reason around the unit circle

Put a circle of radius 1 at the origin. Starting from the positive x-axis, turn counterclockwise through θ. The point is P = (cos θ, sin θ): cosine is its horizontal coordinate and sine its vertical coordinate. These are signed coordinates, not always positive lengths.

At 120°, P = (−1/2, √3/2). In quadrant II, sine is positive and cosine negative, so sin θ > cos θ without finding the exact angle. Pythagoras also gives x² + y² = 1, hence cos² θ + sin² θ = 1 at every angle.